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2 answers:
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Answer:
a) As we can see on the equation given the slope os 1.033 since is the value next to the city mpg (independent variable)
And on this case since the value for the slope is positive the best interpretation is:
E. On the average, highway mileage increases by 1.033 mpg for each additional mpg in city mileage
Because we see the if we increase on 1 unit the city mpg then the highway mpg would increase 1.033
b) For this case as we can see in the model the free term correspond to 6.785 and that correspond to the intercept for this case.
And the best interpretation is given by:
B. Because this is the highway mileage for zero city mpg.
For this reason is not meaningful since we are not interested on 0 or negative city mpg.
c) highway mpg = 6.785 + (1.033 × 18)=25.38 mpg
highway mpg = 6.785 + (1.033 × 25)=32.61 mpg
d) See the figure attached.
Step-by-step explanation:
For this case we have the following linear model:
highway mpg = 6.785 + (1.033 × city mpg)
(a) What is the slope of this line? Say in words what the numerical value of the slope tells us.
As we can see on the equation given the slope os 1.033 since is the value next to the city mpg (independent variable)
And on this case since the value for the slope is positive the best interpretation is:
E. On the average, highway mileage increases by 1.033 mpg for each additional mpg in city mileage
Because we see the if we increase on 1 unit the city mpg then the highway mpg would increase 1.033
(b) What is the intercept? (Enter your answer to three decimal places.)mpgExplain why the value of the intercept is not statistically meaningful.
For this case as we can see in the model the free term correspond to 6.785 and that correspond to the intercept for this case.
And the best interpretation is given by:
B. Because this is the highway mileage for zero city mpg.
For this reason is not meaningful since we are not interested on 0 or negative city mpg.
(c) Find the predicted highway mileage for a car that gets 18 miles per gallon in the city. (Round your answer to two decimal places.)______ mpgFind the predicted highway mileage for a car that gets 25 miles per gallon in the city. (Round your answer to two decimal places.)______ mpg
For this case we just need to replace into the formula and we got:
highway mpg = 6.785 + (1.033 × 18)=25.38 mpg
highway mpg = 6.785 + (1.033 × 25)=32.61 mpg
(d) Draw a graph of the regression line for city mileages between 10 and 50 mpg. (Be sure to show the scales for the x and y axes.)
See the figure attached
The characteristic solution follows from solving the characteristic equation,
so that
A guess for the particular solution may be
, but this is already contained within the characteristic solution. We require a set of linearly independent solutions, so we can look to
which has second derivative
Substituting into the ODE, you have
Therefore the particular solution is
Note that you could have made a more precise guess of
but, of course, any solution of the form
is already accounted for within 
.
so that
A guess for the particular solution may be
which has second derivative
Substituting into the ODE, you have
Therefore the particular solution is
Note that you could have made a more precise guess of
but, of course, any solution of the form